On the planet Oz, there are 8 days in a week- Sunday to Saturday and another…
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On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am.
- A.
89 °
- B.
251 °
- C.
111 °
- D.
79 °
Attempted by 418 students.
Show answer & explanation
Correct answer: A
Final answer: 89°
Key idea: On Oz the hour hand makes two full rotations per day (so one rotation every 18 hours). The minute hand makes one full rotation each hour (90 minutes).
Compute the minute hand angle: (minutes / 90) × 360 = (40/90) × 360 = 160°.
Compute the hour hand angle: one rotation in 18 hours → 360/18 = 20° per hour. Also 20° per hour = 20/90 = 2/9° per minute. Hour angle = hours×20° + minutes×(2/9)° = 12×20 + 40×(2/9) = 240 + 80/9 ≈ 248.89°.
Angle between hands = absolute difference = |248.89° - 160°| ≈ 88.89° ≈ 89°. (The reflex angle would be 360° - 88.89° ≈ 271.11°.)